Mapping forces in 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterize their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the material's microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems

Mapping forces in a 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterise their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the materials microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems. © 2011 Elsevier Ltd. All rights reserved.

Contact dynamics in a gently vibrated granular pile.

We use multispeckle diffusive wave spectroscopy to probe the micron-scale dynamics of a water-saturated granular pile submitted to discrete gentle taps. The typical time scale between plastic events is found to increase dramatically with the number of applied taps. Furthermore, this microscopic dynamics weakly depends on the solid fraction of the sample. This process is largely analogous to the aging phenomenon observed in thermal glassy systems. We propose a heuristic model where this slowing-down mechanism is associated with a slow evolution of the distribution of the contact forces between particles. This model accounts for the main features of the observed dynamics.

Predicting the acoustics of squeak and rattle

This paper discusses the development of a computationally efficient numerical method for predicting the acoustics of rattle events upfront in the design cycle. The method combines Finite Elements, Boundary Elements and SEA and enables the loudness of a large number of rattle events to be efficiently predicted across a broad frequency range. A low frequency random vibro-acoustic model is used in conjunction with various closed form analytical expressions in order to quickly predict impact probabilities and locations. An existing method has been extended to estimate the statistics of the contact forces across a broad frequency range. Finally, broadband acoustic radiation is predicted using standard low, mid and high frequency vibro-acoustic methods and used to estimate impact loudness. The approach is discussed and a number of validation examples are presented.

Prediction of tread block forces for a free-rolling tyre in contact with a rough road

This paper describes a new approach to model the forces on a tread block for a free-rolling tyre in contact with a rough road. A theoretical analysis based on realistic tread mechanical properties and road roughness is presented, indicating partial contact between a tread block and a rough road. Hence an asperity-scale indentation model is developed using a semi-empirical formulation, taking into account both the rubber viscoelasticity and the tread block geometry. The model aims to capture the essential details of the contact at the simplest level, to make it suitable as part of a time-domain dynamic analysis of the coupled tyre-road system. The indentation model is found to have a good correlation with the finite element (FE) predictions and is validated against experimental results using a rolling contact rig. When coupled to a deformed tyre belt profile, the indentation model predicts normal and tangential force histories inside the tyre contact patch that show good agreement with FE predictions. © 2012 Elsevier B.V..

Contact and channel modelling using part and function libraries in a function-based design approach

To support the development and analysis of engineering designs at the embodiment stage, designers work iteratively with representations of those designs as they consider the function and form of their constituent parts. Detailed descriptions of "what a machine does" usually include flows of forces and active principles within the technical system, and their localization within parts and across the interfaces between them. This means that a representation should assist a designer in considering form and function at the same time and at different levels of abstraction. This paper describes a design modelling approach that enables designers to break down a system architecture into its subsystems and parts, while assigning functions and flows to parts and the interfaces between them. In turn, this may reveal further requirements to fulfil functions in order to complete the design. The approach is implemented in a software tool which provides a uniform, computable language allowing the user to describe functions and flows as they are iteratively discovered, created and embodied. A database of parts allows the user to search for existing design solutions. The approach is illustrated through an example: modelling the complex mechanisms within a humanoid robot. Copyright © 2010 by ASME.

Moderate energy impact analysis combining phenomenological contact law with localised damage and integral equation method

A computational impact analysis methodology has been developed, based on modal analysis and a local contact force-deflection model. The contact law is based on Hertz contact theory while contact stresses are elastic, defines a modified contact theory to take account of local permanent indentation, and considers elastic recovery during unloading. The model was validated experimentally through impact testing of glass-carbon hybrid braided composite panels. Specimens were mounted in a support frame and the contact force was inferred from the deceleration of the impactor, measured by high-speed photography. A Finite Element analysis of the panel and support frame assembly was performed to compute the modal responses. The new contact model performed well in predicting the peak forces and impact durations for moderate energy impacts (15 J), where contact stresses locally exceed the linear elastic limit and damage may be deemed to have occurred. C-scan measurements revealed substantial damage for impact energies in the range of 30-50 J. For this regime the new model predictions might be improved by characterisation of the contact law hysteresis during the unloading phase, and a modification of the elastic vibration response in line with damage levels acquired during the impact. © 2011 Elsevier Ltd. All rights reserved.

The analysis of impact forces in randomly vibrating elastic systems

This work is concerned with the characteristics of the impact force produced when two randomly vibrating elastic bodies collide with each other, or when a single randomly vibrating elastic body collides with a stop. The impact condition includes a non-linear spring, which may represent, for example, a Hertzian contact, and in the case of a single body, closed form approximate expressions are derived for the duration and magnitude of the impact force and for the maximum deceleration at the impact point. For the case of two impacting bodies, a set of algebraic equations are derived which can be solved numerically to yield the quantities of interest. The approach is applied to a beam impacting a stop, a plate impacting a stop, and to two impacting beams, and in each case a comparison is made with detailed numerical simulations. Aspects of the statistics of impact velocity are also considered, including the probability that the impact velocity will exceed a specified value within a certain time. © 2012 Elsevier Ltd. All rights reserved.